TC Tailwind

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Emergency Funds Part 3: Modeling Expected and Worst Case Scenarios

In Part 3 of the Emergency Funds series, we look at the hard numbers. I model out just how much money I stand to make and lose in my expected and worst case scenarios, and I share a spreadsheet you can use to do your own modeling.

Graham
12–18 minutes

tl;dr

  • This is a follow up to my previous emergency fund posts: Part 1 and Part 2. In this one, I crunch the numbers on a few interesting scenarios.
  • My expected scenario is: losing my job for 6 months every 10 years, and relying on a Pledged Asset Line to get through it. In this scenario I would end up $47,157 ahead by investing in the S&P 500 instead of an emergency fund, and $32,927 ahead if I invested in a 3-Fund Portfolio (over the course of 10 years).
  • My worst case scenario is: losing my job for a full year, my credit being pulled, and having to sell stocks after the largest S&P 500 drop ever recorded. In this scenario, I would end up:
    • $16,598 behind if I had invested in the S&P 500 and $44,702 ahead if I had invested in a sufficiently large 3-Fund Portfolio, assuming I had enacted my plan 10 years before the crash.
    • $91,636 behind if I had invested in the S&P 500 and $8,989 behind if I had invested in a sufficiently large 3-Fund Portfolio, assuming I had enacted my plan the day before the crash.
  • Coming out ahead in my expected scenario, and not being ruined in the worst case scenario, means that not having an emergency fund matches my risk appetite and is a gamble I’m willing to take (but not necessarily that it’s something you should do!).

Introduction

This post is my attempt to put hard numbers on how much I stand to gain and lose by not having an emergency fund. I get to those numbers by modeling some of the scenarios discussed in Part 2. My whole philosophy around not having an emergency fund is covered in Part 1. This post was written to stand alone, so it’s not strictly required to read the first two posts to understand this one, but they do provide helpful context.

Scenarios

Many of the comments on Part 1 were of the type “what if X happens,” with a lot of people rightfully focusing on worst case scenarios like the Global Financial Crisis (GFC) (discussed in Part 2). Additionally, the feedback almost exclusively focused on what I’d do if I lost my job, so I’ll only be modeling job loss scenarios here. To answer these questions, and to enable folks to run through any scenario they can imagine, I put together this spreadsheet. Anyone can make a copy of it and change the numbers to see if an emergency fund, Pledged Asset Line (PAL), or selling stocks comes out ahead in their scenario. 

Goals

When coming up with scenarios, I can absolutely derive a scenario where having an emergency fund is an obvious choice or a terrible choice, but that won’t tell me much. So to guide the development of scenarios, I think it’s important to consider my goals in not having an emergency fund:

  1. Optimize the expected case: Nothing is certain, but my goal is to give myself the best possible outcomes in the scenarios I consider most likely.
  2. Limit the worst case (within reason): While I always want more money in my bank account, I also want to avoid losses that could bankrupt me, or even losses that could just set back my retirement plans by years. Note that we can always come up with extreme and unlikely scenarios that are impractical to mitigate (eg. what if the US government suddenly refuses to honor any of it’s debts?), so this risk mitigation needs to be tempered with some sense of practicality.

Note that nowhere in these goals did I say I wanted to completely avoid the risk of losses. Risk and reward are generally correlated in investing, so I can’t eliminate risk entirely without also limiting returns. In my mind, some risk is OK, so long as it doesn’t expose you to an unacceptable worst case.

Understanding the Analysis

The spreadsheet I set up compares three main cases:

  1. Having an emergency fund, stored in some safe investment at a lower return. (Labeled “Emergency Scenario“).
  2. Counting on credit to cover you during an emergency, via a PAL or other credit mechanism like a HELOC. This comes with some interest costs. (Labeled “If you relied on a PAL….“).
  3. Counting on selling stocks (ETFs) to cover you during an emergency, even if those stocks have dropped in value significantly at the time of the emergency. This comes with the risk of selling stocks at a market low, locking in losses. (Labeled “If you relied on selling stocks…“).

Each individual parameter is explained in detail in the sheet, but the main concept is built around what I’m calling the “Cycle Time” for the emergency fund. Basically how long, on average, do you expect to hold onto an emergency fund before needing to use it? For example, maybe you expect to deal with a layoff every 10 years. That would lead to a cycle time of ~10 years1. For an emergency fund to be financially optimal in a given scenario, the opportunity cost of holding it for the full cycle has to be less than the cost of dipping into alternative sources of money when an emergency happens. I’m calculating the opportunity cost of an emergency fund as the difference between a “safe” return one would get when investing their emergency fund in something like a high yield saving account vs the expected return of investing that same money in stocks.

Scenario 1 – Expected Case: Out of Work, Relying on a PAL

Setup

In Scenario 1, we assume I lost my job today, and that it would take me 6 months (cell B14) to find a comparable job. The market is doing well and I have access to my PAL, so I don’t cut my expenses and can maintain my $8,000 / month2 (cell B3) in spending. I take it all out of my PAL at a rate of 9.74% (cell B11), racking up $48,000 in debt (cell B18) with another $1,382 in interest (cell B33) on top. I pay that debt down over the following ~6 months (cell B32) once I’ve found a job, racking up another $1,485 in interest (cell B34) in the meantime, for a total of $2,867 in interest paid (cell B35).

If we assume that instead I’d had a 6 month / $48,000 emergency fund, I would have saved that $2,867.54 in interest. If we assume a “cycle time” of 10 years (cell B5), and an expense growth rate of 4% (cell B9 – 2% for inflation, 2% for lifestyle creep), I would have had to have $32,427 (cell B21) in a 6-month emergency fund back in 2014 to cover an equivalent emergency. Assuming my money grew at 1.28% (cell B8 – based on historical 10 return of the FDLXX money market fund) I would have had to put an additional 2.72% / year (cell B24) to maintain the same 6 month buffer as my expenses grew. That growth plus additional deposits would increase my emergency fund each year until it reached the $48,000 I need today. 

Comparing to S&P 500

If instead of having an emergency fund I had invested my money in the S&P 500 at a 9.9% (cell B7) average return, I would have ended up with $83,346 (cell B22). We can also add on the 2.72% a year I could have invested in the S&P 500 instead of using it to top up my emergency fund. Compounding that 2.72% investment gives us another $14,679 (cell B25). Subtracting the $48,000 I would spend during the emergency and the $2,867.54 in interest I’d pay on my PAL, shows that I’d end up $47,157 (cell B37) ahead by investing in the S&P 500 in this scenario. Note that this is a return over the course of 10 years; you could also think of it as $4,715 / year (cell B38) (naively ignoring reinvestment / compounding).

Comparing to a Bogleheads 3 Fund Portfolio

We can also create a modified version of Scenario 1, where we sub in the returns of a Bogleheads 3-Fund Portfolio instead. I don’t have as long performance data on the 3-Fund Portfolio as the S&P 500, but, over the past 30 years a 50% VTI (US stock) / 30% VEU (international stock) / 20% BND (US bonds) fund portfolio had a 8.05% compound annual return. Without making any other changes, punching 8.05% into the spreadsheet (cell B7) shows that I would come out $32,927 (cell B37) ahead by investing in a 3-Fund Portfolio in this scenario. You can think of this as $3,292 / year (cell B38).

Scenario 2 – Worst Case: Out of Work, Market Crashes, PAL Revoked, Needing to Sell Stock at Market Bottom

Setup

In Scenario 2, we consider the old adage “when it rains, it pours”. We assume we’re in a time like the Global Financial Crisis where the S&P 500 has tanked 56%, banks are cutting lending (ie. my PAL gets closed before I can use it), and I’m one of the millions of people that lost their jobs. In this scenario, I’d cut my spending to $6,000 / month3 (cell B3), and would be forced to sell stock to cover my expenses. Given that this is a major financial crisis, we’ll up the assumption of unemployment time to 12 months (cell B14). I’d need $72,000 (cell B18) to cover my costs for the year. 

To fully cover my emergency costs, I would need a $72,000 emergency fund4. Using the same “cycle time” (cell B5 – 10 years), and expense growth (cell B9 – 4%), as the previous example, I would have had $48,640 (cell B21) in my emergency fund back in 2014 and would have had to put in the same 2.72% to keep up with my expense growth.

Comparing to S&P 500

If I was counting on my investment in the S&P 500 to cover me during an emergency, I might get really unlucky and have to sell at the bottom of that 56% (cell B12) drop. To get the $72,000 I need, I’d be selling stock that was recently worth $163,636 (cell B41).

Now some of that $163,636 would come from the growth of the $48,640 + 2.72% I didn’t invest in my emergency fund. Using the same 9.9% (cell B7) average return, that $48,640 would grow to $125,019 (cell B22) before the crash. The 2.72% / year invested in the S&P 500 would compound to $22,019 (cell B25), bringing our total investment value to $147,038. $147,038 is, of course, less than the $163,636 in pre-drop stock I would need to sell to cover my expenses for the year. So in this scenario, not having an emergency means I’d have to sell additional stock that was worth $16,598 (cell 46) pre-drop (though it’d only be worth $7,303 when I sold it, due to the 56% drop). We can debate where the value of the “real” loss sits between $16,598 and $7,303, given that $16,598 is the all-time peak value of the stock that I likely would not have ever sold at, but I’ll be more pessimistic and call it $16,5985.

Comparing to a Bogleheads 3 Fund Portfolio

We can also create a modified version of Scenario 2, where we sub in the returns of a Bogleheads 3-Fund Portfolio instead. We’ll use the same 8.05%6 (cell B7) return discussed above.

The real magic of this scenario, which we discussed briefly in Part 2, is that the bond portion of a 3-Fund portfolio is unlikely to experience the massive 56% drop we modeled for the S&P 500 above. In fact, bonds and stocks have generally been negatively correlated (read: bonds tend to go up when stocks go down) for the past few decades (with 2022 / 2023 being a notable exception). In our worst case of the GFC, BDN’s largest peak-to-trough drop was from $78.61 to $69.96 (11.1%), and it recovered to its pre-drop peak by the end of 2008 (vs the S&P which took until 2013). If I have more than $72,000 of BND in my portfolio (post drop), then I’d be able to exclusively draw on that during the emergency. Relying solely on BND would mean I never have to sell my (presumably much more heavily dropped) stock.

After adjusting returns and expected drop as discussed above, the rest of the calculations are the same as the S&P 500 section. I would need $80,989 (cell B41) in BND pre-drop, to have the $72,000 I need. Compare that to the $105,498 (cell B22) + $20,193 (cell B25) I would have in my 3-Fund portfolio after the 10 years of growth, for a total of $125,691. Thus, I would end up with $44,702 (cell B46) more in (pre-drop) portfolio value by not having an emergency fund.

An important caveat to the above math is that the $125,691 I would have in my 3-Fund portfolio would only have $25,138 of BND in it, at the 20% allocation discussed above. To have the $80,989 of BND I need, my total 3-Fund portfolio would need to be worth at least $404,945.

Scenario 2.5: No “Cycle Time”

The size of the losses or gains in my examples heavily depend on how long of a “cycle time” my invested money gets to grow for. A true worst case scenario would be me enacting my grand plan today, and the market crash + emergency happening tomorrow, rather than 10 years from now. In that scenario:

  1. If I was in the S&P 500: I’d lose the full $163,636 I’d just invested, vs the $72,000 I would have lost if I’d dumped that money in the emergency fund instead. That’s a surplus loss of $91,636, which would hurt a lot, but it wouldn’t leave me destitute nor would it materially impact my retirement plans.
  2. If I was in a 3-Fund Portfolio: I’d lose the full $80,989 of BND vs the $72,000, for a surplus loss of $8,989. That doesn’t feel too bad, all things considered. Note again, however, that this requires me to have at least $404,945 in my 3-Fund Portfolio.

A Note on Assumptions

When attempting to predict the future, you have to make a lot of assumptions, as I’ve done in this post. Where possible, I’ve tried to ground my assumptions in reasonable long term historical data. When there is uncertainty, I always try to bias towards assumptions that favor emergency funds; my goal is to target an “iron man” interpretation of the argument for emergency funds, not a “straw man”. For example:

  1. Assuming a 56% drop in the S&P 500 is the absolute most pessimistic assumption I can make. This is the largest ever difference between the peak and trough of the S&P 500. You’d have to have incredibly bad luck to sell all of your stock on the worst possible day.
  2. Assuming a 9.9% average return in the lead up to the S&P 500 dropping is also a pessimistic assumption. The S&P has an average return of 9.9%, but that includes all of the drops. When looking at pre-drop run up periods, we would expect the S&P to return greater than 9.9%, so that when the drop happens it pulls the average back down to 9.9%.

If any of my assumptions seem off, try changing it in the template and please let me know if a bad assumption materially changed the results!

Conclusions

These scenarios show that not having an emergency fund meets my personal goals (but it’s very possible it might not meet yours!). Namely:

  1. Not having an emergency fund comes out ahead in the case I think is most likely. Obviously nobody can predict the future, but Scenario 1 is the kind of emergency I expect to happen to me a few times in my life.
  2. I can easily survive my worst case for not having an emergency fund. Scenario 2 and 2.5 showed that even when a series of disasters happen, it’s still possible to come out ahead without an emergency fund, but it’s reasonable to expect a loss. Those losses will be much bigger in an all-S&P 500 portfolio than a 3-Fund Portfolio. And even if I don’t come out ahead, the absolute worst case loss is bearable.

Note that we can not conclude whether it’s better to have a 3-Fund or S&P-only Portfolio based on this analysis. Instead, it is only valid to say that if I’ve already decided that a 3-Fund Portfolio is right for me, then a nice benefit is that it is cheaper to rely on as an emergency fund in my worst case scenario. The reason we can’t draw the broader conclusion is that the 3-Fund Portfolio section of Scenario 2 depends on all of my investments (or at least $404,945 of them) being in a 3-Fund Portfolio. Nowhere, however, did we analyze the opportunity cost of moving my entire portfolio from the S&P 500 to a 3-Fund setup. Imagine I had a $10,000,000 portfolio,7 and I moved it from the S&P 500 to a 3-Fund Portfolio because of this example. I’d give up 9.9% – 8.05% = 1.85% returns ($185,000 / year!) to avoid the $16,598 loss discussed above. It’s entirely possible a 3-Fund portfolio is the better option for me8, but it’s not valid to conclude that based on this post!

One final interesting observation is that I can still come out ahead even if I do hit Scenario 2.5. If I realize the gains of Scenario 1 early in my life, and then hit Scenario 2.5 later on, the gains from Scenario 1 may have compounded enough to cover me even in the worst version of Scenario 2 (eg. $47,157 compounded at 9.9% over another 10 years more than covers the worst case surplus loss in Scenario 2.5).

  1. Note that there is some nuance here where the cycle time is the time from creation of emergency fund to the time of using it. If someone is laid off every ten years, they probably use up their emergency fund, and then take some time to reconstitute it. I’m assuming that the reconstitution time is small relative to the total cycle time, so hopefully its impact is small. For those expecting to use their emergency fund very frequently, or expecting to have very little spare income to reconstitute their emergency fund, there are probably enough differences between us that what I’m writing isn’t relevant to them. ↩︎
  2. You might have noticed that this monthly number is higher than the entire emergency fund amount I mentioned in my Part 1. The example I used in my previous post was a real example of a small emergency fund I had back in 2017 when my expenses were much lower. I used that example because I wanted a concrete example of how much I personally missed out on, rather than a theoretical one that had to make a ton of assumptions / guesstimates (like this post does). That seemed to cause a lot of confusion though, so this time around I’m using present day numbers. ↩︎
  3. About $4,000 of my monthly expenses are fixed housing costs, but much of the rest is discretionary. I could easily cut $2,000 a month by dining out less and cutting out travel. ↩︎
  4. I know, very few people keep a full year’s worth of money in an emergency fund. But it’s easiest to compare “everything covered by emergency fund” vs “nothing covered by emergency fund”. In reality, the more likely outcome in this scenario would be that I’d have a smaller emergency fund and it would have run out of money. Once my emergency fund runs out of money, I’d end up selling stocks, just like the non-emergency-fund scenario. Once both scenarios reach the point where I’m selling stock, they are mostly equivalent anyway (assuming you haven’t run out of stock to sell!). ↩︎
  5. Also recall that, as I discussed in Part 2, both losses and gains will compound indefinitely. ↩︎
  6. Note that 8.05% may moderately over estimate the actual returns of a 3-Fund Portfolio in Scenario 2. This overestimation is because the 8.05% number is based on an assumption of rebalancing the portfolio every year on January 1st. When that rebalancing happens at a time where stocks are down and bonds are up (or down less), it has the effect of “buying the dip”. If you withdraw from BND at the exact time of the dip (as Scenario 2 assumes), you miss the opportunity for rebalancing to “buy the dip”, and thus could lower the overall returns. ↩︎
  7. I don’t, but bear with me for the example. ↩︎
  8. I do, in fact, have a version of a 3-Fund Portfolio! ↩︎

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2 responses to “Emergency Funds Part 3: Modeling Expected and Worst Case Scenarios”

  1. Allan Avatar
    Allan

    Have you considered performing this analysis if using the idle funds in your emergency fund to churn bank accounts? For example, banks routinely offer a $750-$1k bonus for opening a savings account and holding $25k for 60-90 days. If you can do this 3-4x per year, you net much more than the typical 5% savings account.

    For example: https://cashbackcow.io/the-bhef-bonus-hunting-emergency-fund/

    Like

    Reply
    1. Graham Avatar
      Graham

      Yeah, that’s a solid way to make an emergency fund make sense! For me personally, I don’t really want to be going through the hassle of constantly opening bank accounts for the bonuses, so that’s not something I personally take on.

      Like

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